System and method for assessing the performance of an attitude control system for small satellites

ABSTRACT

Various embodiments of the present invention include systems and methods for assessing the performance of an actuator of an attitude control system (ACS), such as a control moment gyroscope (CMG). In one embodiment, a system includes a support bracket assembly coupled to an actuator, wherein the actuator is configured to generate an output torque. The system also includes at least one sensor assembly that includes a sensor configured to measure the output torque about at least one axis of the support bracket assembly while the support bracket assembly remains substantially motionless.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation-in-part application of U.S.Non-provisional application Ser. No. 13/809,665, entitled “System andMethod for Assessing the Performance of an Attitude Control System forSmall Satellites,” filed Jan. 11, 2013, which is a national-phase entryof International Application No. PCT/US2011/043128, entitled “System andMethod for Assessing the Performance of an Attitude Control System forSmall Satellites,” filed Jul. 7, 2011, which claims priority to U.S.Provisional Application No. 61/364,264, entitled “System and Method forAssessing the Performance of an Attitude Control System for SmallSatellites,” filed Jul. 14, 2010, the contents of each are herebyincorporated by reference in their entireties.

FIELD OF THE INVENTION

Embodiments of the present invention relate to satellites and, moreparticularly, to systems and methods for assessing the performance of anattitude control system for small satellites.

BACKGROUND

During the past decade there has been growing interest within the spaceindustry towards the development of small satellites. Small satellitesare typically categorized as picosats (1 kg or less), nanosats (1-10kg), microsats (10-100 kg) or minisats (100-500 kg) and range in sizefrom softballs to refrigerators. The interest in these satellites isdriven by the current constraints of traditional satellites and launchsystems. As a result, there has been a significant effort to pushsatellite technology to smaller sizes and mass, which would enable smallsatellites to accomplish missions to complement the larger satellites.Examples of such missions include imaging, remote sensing, surveillance,disaster management, and blue force tracking. These missions areachieved by payloads which demand pointing capabilities from thesatellites. This requires an attitude control system (ACS) with smallactuators that can fit into the volume and mass constraints of smallsatellites.

The two major components of the ACS are the actuator and the controlalgorithm. Various types of actuators include the reaction wheel,magnetic rods, torque coils, thrusters, momentum wheels, and controlmoment gyroscope (CMG). CMGs rotate the angular momentum along aflywheel axis about a gimbal axis to produce a gyroscopic control torqueas shown in FIG. 4( a). The output torque (gyroscopic torque) isamplified over the input torque required to rotate the gimbal axis (dueto the satellite angular velocity) resulting in the well-known torqueamplification factor which allows for higher slew rates. This propertyof torque amplification as well as the fact that CMGs require minimalshaft power, permits the CMG to have a much higher torque per unit massand unit power ratio than RWs.

More specifically, the CMG is a mechanism that produces torque by acombination of two motions—spinning a flywheel about an axis referred toas the flywheel axis and the rotation of the spinning flywheel about anaxis perpendicular to flywheel axis referred to as the gimbal axis. Thetwo main components of a gyroscope are the flywheel and the gimbal. Theflywheel is a spinning rotor with inertia sufficient to provide thedesired angular momentum; the gimbal is a pivot about which the flywheelassembly can be rotated. The magnitude of the gyroscopic torque producedis directly proportional to the inertia of the flywheel, the angularspeed of the flywheel and the rate of rotation of the gimbal. In a CMG,the inertia of the flywheel and the speed of the flywheel are constant,and the torque output is controlled by changing the rotation rate of thegimbal. The direction of the torque produced is perpendicular to boththe flywheel and the gimbal axes per the right hand rule. This torqueacts on the satellite structure to change its attitude. A combination ofgyroscopes is used to produce a net torque in the desired direction andmagnitude. There are various combinations of gyroscopes that can be useddepending upon the mission requirements (box configuration, inlineconfiguration, roof top configuration, pyramidal configuration).

Apart from the gyroscopic torque produced by the CMG, there are othertorques that arise from the motion of the flywheel and gimbal thatcontribute to the dynamics of the satellite:

-   -   Reaction torque due to friction in the flywheel bearings.    -   Reaction torque due to the acceleration of the gimbal; this        torque depends on the angular acceleration and the inertia of        the gimbal.    -   Reaction torque due to the friction of the gimbal bearings and        slip ring.

The motion to the flywheel and gimbal is provided by flywheel and gimbalmotors. There are feedback devices (e.g., encoders and Hall-effectsensors) for sensing the angular speed and position. A slip ring isprovided for continuous power supply to the flywheel motor for endlessrotation of the gimbal. All these hardware are assembled together withstructural components.

The output torque of the actuator is used to evaluate its performance.Certain kinds of actuators that use momentum from spinning wheels togenerate torque are prone to disturbances due to misalignments andnon-homogeneity of the wheels. This disturbance is termed as jitter.These actuators which contain wheels are evaluated for torque output andjitter as their performance metrics. Although there exists test bedsthat can evaluate the performance of large actuators, there has not beento date, an instrument to determine the performance of miniatureactuators (<5 Nmm torque capacity).

ACSs are one of the most challenging spacecraft sub-systems for hardwareperformance verification and validation. Testing of ACSs pose manychallenges as it requires simulation and control of spacecraft responseto actuator inputs. Traditionally, this has been achieved using a motionplatform that has three rotational degrees-of-freedom (dof) to emulatethe spacecraft's attitude motion. ACS test beds developed to date forvarious institutions (e.g., Georgia Tech, NPS, Honeywell, AFRL to name afew) are typically for large spacecraft (>500 kg) and all, withoutexception, are suspension-based systems using air bearings¹. Althoughthese test beds have provided a means to validate 3-axis attitudecontrol systems, they are limited in their testing capabilities and haveseveral disadvantages. For example, ACS test beds using air bearingshave limited range of motion about the pitch and roll axes (about±30°)², rendering the tests of continuous large angle maneuversimpossible. These test beds also have limits on their rotational ratesas the centrifugal forces due to rotation have to be less than thedynamic capacity of the air bearing, i.e., these test beds limit theangular velocity of the simulated spacecraft thus preventing rapidretargeting maneuvers. Additionally, in order to nullify the bias torquedue to gravity, these test beds require an additional dynamic massbalancing system which requires a separate control system³. Thereactions due to the movement of the balancing masses induce unwanteddisturbances to the spacecraft dynamics. There are additionaleffects/disturbances due to gravity sag associated with the size ofthese structures, viscous drag of the atmosphere, and the air draft fromclean room blowers. Another major shortcoming of these test beds is thatthey cannot be used to test in an environmental chamber (thermal/vacuum)due to their complex nature and their dependency on air bearing. It ishence impossible to characterize the operational performance of thesystem under test in a representative space environment. FIG. 1( a)shows the schematic of a conventional test bed in which all thenecessary hardware has to be integrated onto the air bearing platform.It should be noted that due to the platform's motion, an attitudedetermination system (ADS) is required onboard the air bearing test bed.ACS test beds for small satellites pose even harder challenges sincethey are more prone to viscous drags and other environmentaldisturbances due to their small inertia. Furthermore, it is difficult toincorporate a mass balancing system within the mass and inertia limitsof these test beds. While there have been efforts in development ofcontrol strategies and actuators, there has been no transformativeeffort in the testing methods of attitude control system for the pastfifty years¹. There are currently no such test beds available for smallsatellites, especially for the pico (1 kg) and nano (10 kg) class.

Therefore, there exists a need for a system and method for assessing theperformance of ACSs for satellites (e.g., pico and nano-satellites). Itwould be further advantageous for a system and method for assessing theperformance of a CMG.

BRIEF SUMMARY OF THE INVENTION

Embodiments of the present invention are directed to systems and methodsfor assessing the performance of actuators for attitude control ofsatellites, such as small satellites (e.g., pico and nano-satellites).In one embodiment, a system includes a support bracket assembly coupledto an actuator (e.g., a CMG), wherein the actuator is configured togenerate an output torque. The system also includes at least one sensorassembly coupled to the support bracket assembly, wherein the at leastone sensor assembly includes a sensor configured to measure an outputtorque of the actuator about at least one axis of the support bracketassembly (e.g., a pitch or a roll axis) while the support bracketassembly remains substantially motionless. For example, the supportbracket assembly is configured to deflect less than about 30 arc minuteswhile the sensor measures the output torque about the at least one axis.In another embodiment, the system is configured to measure the outputtorque about a plurality of axes of the support bracket assembly (e.g.,a pitch and a roll axis). The system may further include a dataacquisition system in communication with the at least one sensorassembly and that is configured to receive the measured output torque.

According to aspects of the invention, the support bracket assemblyincludes a pitch axis gimbal coupled to the actuator. The supportbracket assembly may further include a roll axis gimbal pivotablycoupled to the pitch axis gimbal. The pitch axis gimbal may be mountedinternally with respect to the roll axis gimbal. The pitch axis gimbaland the roll axis gimbal may extend in perpendicular planes with respectto one another (e.g., vertical and horizontal planes respectively). Thesensor may be a pitch axis sensor coupled to the pitch axis gimbal andconfigured to measure torque on the pitch axis gimbal. The sensorassembly may further include a shaft extending through the roll axisgimbal and coupling the pitch axis gimbal and the pitch axis sensor. Thesensor assembly may include a pitch axis sensor bracket coupled to theroll axis gimbal and configured to support the pitch axis sensor.

According to additional aspects, the sensor assembly includes a rollaxis sensor coupled to the roll axis gimbal and is configured to measuretorque on the roll axis gimbal. The support bracket assembly may furtherinclude a support bracket, wherein the roll axis gimbal is pivotablycoupled to the support bracket. The at least one sensor assembly mayalso include a shaft extending through the support bracket and couplingthe roll axis gimbal and the roll axis sensor. Furthermore, the sensorassembly may include a roll axis sensor bracket coupled to the supportbracket and configured to support the roll axis sensor.

According to another embodiment, a method for assessing the performanceof an actuator (e.g., a CMG) of an attitude control system is provided.The method includes coupling an actuator to a support bracket assemblyand generating an output torque with the actuator. The method furtherincludes coupling at least one sensor to at least a portion of thesupport bracket assembly. The method further includes measuring theoutput torque of the actuator about at least one axis of the supportbracket assembly with the at least one sensor while the support bracketassembly remains substantially motionless. Aspects of the method includemeasuring the output torque of the actuator about each of a plurality ofaxes of the support bracket assembly (e.g., a pitch and a roll axis).

According to another embodiment, a system includes a support bracketassembly coupled to an actuator (e.g., a CMG), wherein the actuator isconfigured to generate an output torque. The system also includes atleast one sensor assembly that includes a sensor configured to measurean output torque of the actuator about at least one axis of the supportbracket assembly (e.g., a pitch or a roll axis) while the supportbracket assembly remains substantially motionless. For example, thesupport bracket assembly is configured to deflect less than about 30 arcminutes while the sensor measures the output torque about the at leastone axis. In another embodiment, the system is configured to measure theoutput torque about a plurality of axes of the support bracket assembly(e.g., a pitch axis and a roll axis). The system may further include adata acquisition system in communication with the at least one sensorassembly and that is configured to receive the measured output torque.

According to aspects of the invention, the support bracket assemblyincludes a pitch axis gimbal coupled to the actuator. The supportbracket assembly may further include a roll axis gimbal pivotablycoupled to the pitch axis gimbal. The pitch axis gimbal may be mountedinternally with respect to the roll axis gimbal.

In some embodiments, the at least one sensor assembly comprises at leastone torque sensor coupled to at least a portion of the support bracketassembly and configured to measure the output torque. According to otheraspects, the sensor assembly includes at least one laser sensorconfigured to measure displacement of the pitch axis gimbal. Thedisplacement of the pitch axis gimbal is representative of the outputtorque on the pitch axis gimbal. In another embodiment, the at least onesensor assembly further comprises a second laser sensor configured tomeasure displacement of the roll axis gimbal. The displacement of theroll axis gimbal is representative of the output torque on the roll axisgimbal.

In some embodiments, the at least one sensor assembly comprises a lasersensor configured to measure displacement of at least a portion of thesupport bracket assembly, wherein the displacement of the portion of thesupport bracket assembly is representative of the output torque about atleast one axis of the support bracket assembly.

According to another embodiment, a method for assessing the performanceof an actuator (e.g., a CMG) of an attitude control system is provided.The method includes coupling an actuator to a support bracket assemblyand generating an output torque with the actuator. The method furtherincludes measuring the output torque of the actuator about at least oneaxis of the support bracket assembly with the at least one sensor whilethe support bracket assembly remains substantially motionless.Additional aspects of the method include measuring the output torque ofthe actuator about each of a plurality of axes of the support bracketassembly (e.g., a pitch and a roll axis).

According to one embodiment, the method further comprises coupling atleast one sensor to at least a portion of the support bracket assembly.Additionally, the measuring step comprises measuring the output torquewith a torque sensor. According to another embodiment, the measuringstep comprises measuring the displacement of a portion of the supportbracket assembly with a laser sensor. The displacement of the portion ofthe support bracket assembly is representative of the output torqueabout at least one axis of the support bracket assembly

BRIEF DESCRIPTION OF THE DRAWINGS

Reference will now be made to the accompanying drawings, which are notnecessarily drawn to scale, and wherein:

FIG. 1( a) illustrates a schematic of a conventional test bed;

FIG. 1( b) illustrates a schematic of a system for assessing performanceof an actuator according to one embodiment of the present invention;

FIG. 2 illustrates a flowchart of a method for assessing performance ofa CMG according to one embodiment of the present invention;

FIG. 3 illustrates a flowchart of a method for assessing performance ofa CMG according to one embodiment of the present invention;

FIGS. 4( a)-4(c) illustrate CMGs according to various embodiments of thepresent invention;

FIG. 5 shows an exploded view of a CMG according to one embodiment ofthe present invention;

FIG. 6 depicts a system for assessing performance of a CMG according toone embodiment of the present invention;

FIG. 7 depicts a system for assessing performance of a CMG according toanother embodiment of the present invention;

FIG. 8 illustrates a system for assessing performance of a CMG accordingto one embodiment of the present invention;

FIGS. 9-14 illustrate various views of a prototype system for assessingperformance of a CMG according to one embodiment of the presentinvention;

FIGS. 15-20 show various test results of the system shown in FIGS. 9-14;

FIG. 21 depicts a system for assessing performance of a CMG according toanother embodiment of the present invention;

FIG. 22 depicts a system for assessing performance of a CMG according toanother embodiment of the present invention;

FIG. 23 shows test results of the system shown in FIG. 22;

FIG. 24 illustrates a star field simulator according to one embodimentof the present invention;

FIG. 25 illustrates a flow chart of a method for updating the star fieldsimulator shown in FIG. 24;

FIG. 26 illustrates a magnetic field simulator according to oneembodiment of the present invention; and

FIG. 27 illustrates a flow chart of a method for updating the magneticfield simulator shown in FIG. 26.

DETAILED DESCRIPTION OF VARIOUS EMBODIMENTS OF THE INVENTION

Various embodiments of the present invention will now be described morefully hereinafter with reference to the accompanying figures, in whichsome, but not all embodiments of the inventions are shown. Indeed, theseinventions may be embodied in many different forms and should not beconstrued as limited to the embodiments set forth herein. Rather, theseembodiments are provided so that this disclosure will satisfy applicablelegal requirements. Like numbers refer to like elements throughout.

Embodiments of the present invention are directed to a system and methodfor assessing the performance of an ACS actuator such as a CMG for smallsatellites (e.g., pico and nano-satellites). In one embodiment, thepresent invention facilitates 3-axis testing of ACSs in any desiredenvironment, although testing of one or more axes is also contemplated.FIG. 1( b) illustrates a schematic of one embodiment of a system 10 forperforming such testing, wherein the system 10 includes test bedhardware 12 (e.g., attitude control actuators, torque sensors, driveelectronics, sensor electronics, electrical power) and software 14(e.g., ADCS algorithms, attitude propagator, and satellite dynamicmodel). The output torque is sensed using a testing system and then usedin simulation of the spacecraft dynamic motion.

Most of the shortcomings of conventional air bearing based test bedsarise from the fact that motion is required for the functioning of theseplatforms. One advantage of embodiments of the present invention is touse a motionless torque sensing platform to characterize the outputtorque of the attitude control actuators. In particular, the embodimentsof the present invention do not require simulating motion of a satelliteor spacecraft. Thus, the system is configured to be “motionless” or“substantially motionless” while measuring the output torque of theactuator. For example, substantially motionless can be defined bydeflection of less than about 30 arc minutes. Although the followingdiscussion relates to assessing the performance of a CMG, it isunderstood that the system may be configured to assess the performanceof other actuators for ACSs. In addition, although embodiments of thepresent invention facilitate testing of a system about at least oneaxis, the system may be configured to measure output torque about atleast one axis or a plurality of axes of the system. Moreover,embodiments of the present invention are adaptable for use with smallsatellites as discussed above, but may also be adaptable for largersatellites taking into consideration the necessary scalingconsiderations.

Generally, the CMG 30 includes a flywheel assembly 32, a gimbal assembly34, and a slip ring assembly 36, as shown in FIGS. 4( b) and 5. Onefunction of the flywheel assembly 32 is to accommodate one or morespinning flywheels 38 and its motor 40 that provide the required angularmomentum to the CMG. The flywheel assembly 32 also provides an interfaceto the gimbal assembly 34. The gimbal assembly 34 is configured tofacilitate the rotation of the entire flywheel assembly 32 about thegimbal axis. The gimbal assembly 34 includes a bracket 44 and a gimbalmotor plate or housing 46. The bracket 44 and the gimbal motor housing46 support the pivoting of the flywheel assembly 32. A plurality of CMGsmay be coupled together in various configurations (e.g. pyramidal asshown in FIG. 4( c)) for use with satellites. For more details regardingexemplary CMGs and associated satellites, please see InternationalApplication No. PCT/US2010/035397, entitled Attitude Control System forSmall Satellites, filed on May 19, 2010, which is incorporated byreference in its entirety herein.

Exemplary parameters of interest to characterize and verify performanceof an attitude control system are the pointing accuracy, jitter, slewrates, and torque output. All of these parameters are a function of thetorque produced by the attitude actuator. In traditional air bearingtest beds, the actuator would enable the movement of some of thecomponents of the spacecraft along with the test bed itself on an airbearing. The pointing accuracy, jitter, and slew rate of the spacecraftare directly measured using onboard sensors. Spacecraft dynamic modelsare usually available accurately when the control system is beingdesigned. If the output torque of the attitude actuator can be measuredin real time, then this torque can be used as an input to the spacecraftdynamic model for simulating the same behavior as that of a test bed onan air bearing. This would eliminate the need for physical motion of thespacecraft (or components) and onboard sensors.

FIG. 2 shows a schematic implementation strategy of a system 20according to one embodiment of the present invention. This method can beimplemented for testing a pyramidal cluster of CMGs. The CMG cluster ismounted onto an interface of the system 20 which measures the threedimensional torque output of the CMGs 22. The measured torque along withactuator feedback signals are passed through a signal conditioner andconverted into discrete data by a high frequency data acquisition unit24. The measured torque is input to a spacecraft dynamic model 26 on acomputer. The response of the spacecraft is captured by simulation ofthe dynamic model and the attitude is propagated using another piece ofsoftware 28 that uses the output of the simulation. The attitudepropagation can also include ADS hardware in the loop if desired, toperform integrated attitude determination and control (ADCS) testing.The computed attitude error is used by the ACS algorithms 30 to commandinput to the actuators.

Equations of Motion

The CMG produces torque by redistribution of angular momentum; it is adevice that stores angular momentum in its flywheels and produces atorque by changing the direction of the flywheel axis or the angularmomentum vector. The equation of motion that governs this characteristicis developed below.

Nomenclature

H _(G) Total angular momentum of the CMG about the gimbal center of mass

H _(G) ^(f) Angular momentum of the flywheel about the gimbal center ofmass

H _(G) ^(g) Angular momentum of the gimbal about the gimbal center ofmass

I ^(f) Inertia of the flywheel

I ^(g) Inertia of the gimbal

ω^(f) Angular velocity of the flywheel

{dot over (ω)} ^(f) Angular acceleration of the flywheel

ω ^(s) Angular velocity of the spacecraft

{dot over (δ)} Angular velocity of the gimbal

{umlaut over (δ)} Angular acceleration of the gimbal

τ ^(d) Total dynamic torque produced by the CMG

τ ^(gy) Total gyroscopic torque produced by the CMG

τ ^(fa) Torque due to flywheel acceleration

τ ^(ga) Torque due to gimbal acceleration

The total angular momentum of the CMG,

H _(G) =H _(G) ^(f) +H _(G) ^(g)

H _(G) =I ^(f) ω ^(f) +I ^(g){dot over (δ)}  (1)

Where H _(G) ^(f) and H _(G) ^(g) the angular momenta of the flywheeland the gimbal respectively about the gimbal center of mass, I ^(f) andI ^(g) are the inertias of the flywheel and gimbal respectively, ω ^(f)and {dot over (δ)} are the angular velocities of the flywheel and thegimbal respectively. From Euler's law, the rate of change of angularmomentum is equal to the torque acting on the system.

$\begin{matrix}{\mspace{79mu} {{{\frac{}{t}\left( {\underset{\_}{H}}_{G} \right)} = {{\frac{}{t}\left( {{\underset{=}{I}}^{f}{\underset{\_}{\omega}}^{f}} \right)} + {\frac{}{t}\left( {{\underset{=}{I}}^{g}\overset{.}{\underset{\_}{\delta}}} \right)} + {\left( {\overset{.}{\underset{\_}{\delta}} + {\underset{\_}{\omega}}^{s}} \right) \times \left( {{{\underset{=}{I}}^{f}{\underset{\_}{\omega}}^{f}} + {{\underset{=}{I}}^{g}\overset{.}{\underset{\_}{\delta}}}} \right)}}}{{\frac{}{t}\left( {\underset{\_}{H}}_{G} \right)} = {{\frac{}{t}\left( {{\underset{=}{I}}^{f}{\underset{\_}{\omega}}^{f}} \right)} + {\frac{}{t}\left( {{\underset{=}{I}}^{g}\overset{.}{\underset{\_}{\delta}}} \right)} + {\overset{.}{\underset{\_}{\delta}} \times \left( {{\underset{=}{I}}^{f}{\underset{\_}{\omega}}^{f}} \right)} + {{\underset{\_}{\omega}}^{s} \times \left( {{{\underset{=}{I}}^{f}{\underset{\_}{\omega}}^{f}} + {{\underset{=}{I}}^{g}\overset{.}{\underset{\_}{\delta}}}} \right)}}}}} & (2) \\{\mspace{79mu} {{\frac{}{t}\left( {\underset{\_}{H}}_{G} \right)} = {{\underset{\underset{{Flywheel}{Acceleration}}{}}{{\underset{=}{I}}^{f}{\overset{.}{\underset{\_}{\omega}}}^{f}} + \underset{\underset{{Gimbal}{Acceleration}}{}}{{\underset{=}{I}}^{g}\overset{¨}{\underset{\_}{\delta}}} + \underset{\underset{{Gyroscopic}({control})}{}}{\overset{.}{\underset{\_}{\delta}} \times \left( {{\underset{=}{I}}^{f}{\underset{\_}{\omega}}^{f}} \right)} + {{\underset{\_}{\omega}}^{s} \times {\underset{\_}{H}}_{G}}} = {\underset{\_}{\tau}}^{d}}}} & (3)\end{matrix}$

{umlaut over (δ)} is the angular acceleration of the gimbal, ω ^(s) isthe angular velocity of the spacecraft and τ^(d) is the total dynamictorque output of the CMG. Equation (3) is the governing equation for thedynamic torque produced by the CMG. Torque due to flywheel and gimbalaccelerations are not used for control and are unwanted consequenceswhich occur during start and stop of flywheel and gimbal motion; it isideal to have the torques due to flywheel and gimbal accelerations to bezero.

The total dynamic torque produced by all four CMGs is given by

$\begin{matrix}{{\underset{\_}{\tau}}^{d} = {\sum\limits_{i = 1}^{4}\; {\underset{\_}{\tau}}^{di}}} & (4)\end{matrix}$

Attitude Control Testing Architecture

A single unit of CMG produces torque proportional to the gimbal speedand lies on plane as was shown in the previous section. The torque spanof a pyramidal CMG arrangement belongs to

³. In one embodiment, a three axis torque sensor is required todetermine the output of the pyramidal cluster. The hardware and softwarearchitecture of a system 50 according to one embodiment is shown in FIG.3. The torque output of the CMGs may be measured using a tri-axialtorque sensor 52. The output of the torque sensor 52 is passed through asignal conditioner 54 with a built in filter and acquired using a dataacquisition unit 56. The sampled data is further filtered and scaledbased on the sensitivity of the transducer. The output torque is now fedinto the spacecraft dynamic model 58 (e.g., via Simulink on a computer).The response of the spacecraft (angular velocity of the spacecraft) isused in an attitude propagation algorithm 60 to determine the attitudeof the spacecraft. The misalignment between the desired attitude andmeasured attitude of the spacecraft is the attitude error and is fedinto the attitude control algorithm 62. The attitude control algorithm62 determines the required torque, and the CMG steering logics 62determine the appropriate gimbal rates and accelerations to be commandedto achieve this torque. The gimbal rates and accelerations are commandedto the CMG gimbal motors. In the case of CMG testing, it is noted thatthe spacecraft angular velocity affects the performance of the CMG as itproduces a gyroscopic torque on the gimbals (the ω ^(s)×H _(G) term inEq. (3), represented by τ^(s) in FIG. 3). This torque is not naturallycaptured in the aforementioned technique as it would have been in airbearing test beds as the CMGs are not on a moving platform that emulatesspacecraft motion. This issue may be addressed using the torquecompensation technique—the torque on the gimbals can be computed usingthe CMG flywheel angular velocity (feedback from CMG) and spacecraftangular velocity (output of spacecraft dynamic model); this torque issubtracted from the output torque of the CMGs before it is sent as aninput to the spacecraft dynamic model.

System Design

The system design discussed below is for a single axis version with abuilt in capacity to be extended to a two axis version. The same conceptcan be extended to design two or more axis versions. Thus, although thediscussion below relates to a single axis system, the system may bemodified for use with a plurality of axes in alternative embodiments.

FIG. 6 shows a system 70 with a CMG 72 mounted thereon according to oneembodiment of the present invention. The system 70 generally includes asupport bracket assembly 71 and at least one sensor assembly 73. Thesupport bracket assembly 71 includes a pitch axis gimbal 74 pivotallycoupled to a roll axis gimbal 76. The pitch axis gimbal 74 is configuredto pivot with respect to the roll axis gimbal 76. The pitch axis gimbal74 is aligned in a generally vertical plane, while the roll axis gimbal76 is aligned in a generally horizontal plane. The gimbals 74, 76 may bemade of various materials, such as aluminum, and are designed to havevery low inertia. The pitch axis gimbal 74 is mounted inside the rollaxis gimbal 76, wherein the gimbals may be rectangular or other shapeswith respective openings for accommodating and supporting the CMG 72therein. The pitch axis gimbal 74 comprises an actuator mount bracket 88to which the CMG can be attached, thereby facilitating transfer of theoutput torque of the CMG to the support bracket assembly 71. It is ofnote that the CMG is capable of its full range of motion due to itspositioning within the support bracket assembly. Thus, the system isconfigured for testing the CMG over its entire range of motion.

The pitch axis gimbal 74 and roll axis gimbal 76 may be coupled via apair of inner gimbal pivots 77 extending along a pitch axis of thesupport bracket assembly 71. In the illustrated embodiment, the innergimbal pivots 77 may be small stainless steel shafts coupled to thepitch axis gimbal 74. The shafts may be located on small low frictionbearings (friction coefficient<0.01) mounted on the roll axis gimbal 76.One of the shafts, or transducer coupler shaft 80, is longer than theother and projects through the roll axis gimbal 76.

The roll axis gimbal 76 is mounted on a pair of outer gimbal pivots 78along a roll axis of the support bracket assembly 71 in a similar manneras the inner gimbal pivots 77. In this regard, the roll axis gimbal 76is coupled to a support or U-shaped bracket 82 via the inner gimbalpivots 78. However, the support bracket 82 is stationary and is fixed toa rigid isolated platform 84. The rotation of the roll axis gimbal 76about these pivots 78 is locked using fasteners for a single axismeasurement. This locking can be removed to extend the testing totwo-axis as explained in further detail below.

The sensor assembly 73 includes a pitch axis sensor bracket 86 ortransducer bracket, which may be L-shaped. The transducer bracket 86 maybe attached to the roll axis gimbal 76 on the side through which thetransducer coupler shaft 80 extends. A highly sensitive transducersensor 90 capable of measuring small torques is mounted on thetransducer bracket 86 with the measuring shaft pointing towards thegimbals 74, 76. The arrangement is such that the transducer shaft iscollinear with the transducer coupler shaft 80 with some axial spacingsufficient to accommodate a flexible coupling 92. A suitable coupling 92with high torsional stiffness but low bending stiffness is chosen tocouple the transducer shaft and the transducer coupler shaft 80. Thebending flexibility accommodates any misalignments between the twoshafts without damaging the sensitive transducer shaft. Once thiscoupling is fixed, the pitch axis gimbal 74 cannot rotate freely and isconstrained by the transducer shaft. Any torque applied on the pitchaxis gimbal 74 about the pitch axis is now measured by the transducer 90while the support bracket assembly 71 remains substantially motionless.A similar transducer can be used on the roll axis gimbal to obtain twoaxis torque measurements as explained below.

According to another embodiment, a system 100 for measuring outputtorque about two axes is illustrated in FIG. 7 and may be used tocharacterize the performance of a CMG 72. As before, the system 100 alsoincludes a pitch axis gimbal 74 and a roll axis gimbal 76. The pitchaxis gimbal 74 may be pivotally mounted on the inside of the roll axisgimbal using low friction bearings. The roll axis gimbal 76 is alsopivotally coupled to the support bracket 82, such as via low frictionbearings. In this embodiment, a plurality of sensor assemblies 73 areprovided. The second sensor assembly 73 includes a roll axis sensor ortransducer 102 mounted on the support bracket 82. This transducer 102measures any torque about the roll axis. The CMG 72 is mounted such thatits torque output lies in the plane formed by the pitch and the rollaxes of the support bracket assembly 71. The sensor assemblies 73 arecapable of measuring the torque output of the CMG about the pitch andthe roll axes while the support bracket assembly 71 remainssubstantially motionless. The system 100 is scalable or otherwiseadaptable for different actuators through the exchange of the torquetransducers for measuring the appropriate torque. The bias torque due tothe overhanging transducer 90, 102 is constant as the setup ismotionless and can be either removed by static balancing or by negatingthe bias from the measurement. The torque due to the change in center ofmass location of CMG 72 can be calculated from the position of thegimbals 74, 76 and can be taken into account in the scaling before inputto the spacecraft dynamic model.

System Design with Three Axes

As noted above, the system design described herein may extend to anynumber of axes. For example, in some embodiments, a system 200 formeasuring output torque about three axes is illustrated in FIG. 21 andmay be used to characterize the performance of a CMG 272. As before, thesystem 200 also includes a pitch axis gimbal 274 and a roll axis gimbal276. In addition, however, the system 200 further includes a yaw axisgimbal 278. The pitch axis gimbal 274 may be pivotally mounted on theinside of the roll axis gimbal 276 using low friction bearings. The rollaxis gimbal 276 is also pivotally coupled on the inside of the yaw axisgimbal 278 using low friction bearings. Further, the yaw axis gimbal 278is pivotally coupled to a support bracket 282, such as via low frictionbearings.

In this embodiment, a plurality of sensor assemblies 284, 286, 288 areprovided. The first sensor assembly 284 includes a pitch axis sensor ortransducer coupled to the roll axis gimbal and configured to measuretorque about the pitch axis. The second sensor assembly 276 includes aroll axis sensor or transducer coupled to the yaw axis gimbal 278 andconfigured to measure torque about the roll axis. The third sensorassembly 288 includes a yaw axis sensor or transducer coupled to thesupport bracket assembly 282 and configured to measure torque about theyaw axis. The CMG 272 is mounted such that its torque output lies in theplane formed by the pitch, roll, and yaw axes of the support bracketassembly 282. The sensor assemblies 284, 286, 288 are capable ofmeasuring the torque output of the CMG about the pitch, roll, and yawaxes while the support bracket assembly 282 remains substantiallymotionless. The system 200 is scalable or otherwise adaptable fordifferent actuators through the exchange of the torque transducers formeasuring the appropriate torque. The bias torque due to offsets ofcenter of mass (e.g., from the overhanging transducers) are constant asthe setup is motionless and can be either removed by static balancing orby negating the bias from the measurement. The torque due to the changein center of mass location of CMG 272 can be calculated and can be takeninto account in the scaling before input to a spacecraft dynamic model.

Measurement Technique

FIG. 8 shows a test setup for measuring the output torque of a CMGaccording to one embodiment of the present invention. A CMG is mountedon the pitch axis gimbal via an actuator mounting bracket. Any torqueproduced by the CMG about the pitch axis is measured by the transducer.The torque transducer is connected to a data acquisition system via asignal conditioner. The output voltage of the signal conditioner, whichis a measure of the torque being measured by the transducer is sampledby the data acquisition system and may be stored on a computer foranalysis. The CMG may be controlled via a motor controller. The wiresconnecting the CMG to the motor controller are preferably a very thingauge as it can cause additional torque on the transducer. The designcan include a slip ring that will mitigate this issue.

Prototype and Test Results

A prototype system of a single axis version is shown in FIGS. 9-14.Several tests were conducted before and during the testing to understandthe system. Various exemplary steps may be performed prior to beginningtesting. For example, the CMG is typically mounted on the supportbracket assembly before mounting the sensor, and the data acquisitionsystem may be connected to the sensor during assembly so that the torqueof the sensor can be monitored. The roll axis gimbal is fixed withfasteners, and the gimbal motor and flywheel motor control board (viaslip rings) are connected to the motor driver board. The motor driverboard is powered with an adequate power supply (e.g., 5V DC motor),while the signal conditioner and data acquisition system also include apower source (e.g., 110 V). The sensor is then connected to the signalconditioner and the data acquisition unit, and the computer isconfigured to record the sensor output in real time. The power to themotor driver board and flywheels are rotated at a constant speed, suchas 4500 rpm. The gimbals may also be rotated at a constant speed, suchas 0 to 2 rad/s. The torque output and gimbal speed is recorded. Thetest may be repeated for different gimbal and/or flywheel speeds. Therecorded values may then be compared to theoretical values for furtheranalysis.

Noise Analysis

The torque transducer was connected to a data acquisition systemsampling at 1000 Hz. Data was taken without loading the transducer toanalyze the transducer and the environmental noise characteristics. Thistest would also identify any bias in the transducer output. A FastFourier Transform (FFT) was performed on the data acquired to identifyif the noise was random. FIG. 15 shows the data recorded and its FFT. Itis shown that the mean of the recorded data is zero. The FFT shows thatthe amplitude of the spectrum is almost evenly spread over allfrequencies except for some peaks. One evident peak is from the 60 Hzelectrical noise. Another peak at about 230 Hz is due to a fan on thecomputer of the data acquisition system.

Mean Value/Bias Analysis

The torque transducer was mounted on the system with the CMG turned off.The data was recorded to determine any bias torque (static torque)acting on the transducer due to center of mass offset from the pitchaxis of the gimbal. The recorded data is shown in FIG. 16 and the meanof the data is calculated to be about 0.6717 Nmm. This value issubtracted from the measurements during the torque test of the CMGs.

Gimbal Shaft—Coupling—Transducer Shaft Drive System Analysis

The transmission from the pitch axis gimbal to the transducer straingauges via the gimbal shaft, flexible coupling, and the transducer shafthas its own dynamics approximated to be of second order. A test was doneto identify the natural frequency of this system and be sure that it isnot in the range of the operating frequency of the CMG flywheel. Toperform this test, the pitch axis gimbal was slightly disturbed byimpacting it lightly by hand. Data was taken until the oscillationssettled out. An FFT was performed on this data to identify the naturalfrequency of the system. FIG. 17 shows the recorded data and its FFT. Itcan be seen that the natural frequency of this system is about 10 Hzwhich is much less than the normal flywheel speed of 75 Hz.

Torque Output at Flywheel Start

The flywheel axis is aligned with the pitch axis by rotating the gimbal.The flywheel is started while the data from the torque transducer isbeing recorded. This test will capture the torque output due to theacceleration of the flywheel as shown in Equation(3). This torquemeasurement is important in the development of the ACS. Data arerecorded even after the flywheel reaches its maximum speed and isspinning continuously at this speed. This is done in order to quantifythe disturbance created by the flywheel acceleration while trying tomaintain constant speed and overcoming friction. The plot of themeasured data and its FFT are shown in FIG. 18. The flywheel wasswitched on at about 22 s. It can be seen that there are peaks at about10, 75, 150, 225 and 300 Hz. The 10 Hz peak is due to the naturalfrequency of the system identified above. This occurs when the flywheelaccelerates imparting instantaneous torque onto the system and then runat constant speed similar to impacting the pitch axis gimbal. The peakat 75 Hz is due to the control speed of the flywheel at 4500 rpm. Thepeak at 150, 225 and 300 Hz are due to the friction in the bearingshowing up as multiples of the flywheel speed. FIG. 18 shows that thedynamics of the measurement system is coupled with the CMG dynamics.Hence the flywheel startup torque output, even though a step appears asoscillatory torque in the measurements.

Torque Output at Gimbal Speed of 1 Hz

This test measures the gyroscopic torque output of the CMG as set forthin Equation(3). The gyroscopic torque is perpendicular to the flywheeland the gimbal axis. The transducer measures the maximum torque when theflywheel axis is perpendicular to the pitch axis of the system. Itmeasures the pitch axis component of the torque elsewhere. Hence theoutput torque profile should look like a sinusoid with a frequency equalto the gimbal rotating frequency. The torque output measurement is shownin FIG. 19. It can be seen that the measurement follows the theoreticalvalues closely. The downward slope on the sinusoid is steeper than thepositive slope as there may have been a misalignment in the gimbal axiswhich caused wobble and lower frictional resistance on one half of thecycle.

FIG. 20 shows the FFT of the torque output shown in FIG. 19. The peaksin the plot have been labeled in the figure. The first peak is shown at0 Hz and this is due to the bias torque on the transducer. The secondpeak occurs at the frequency of the gyroscopic torque which is equal tothe gimbal speed of 1Hz. The third peak occurs at a frequency abouttwice the gimbal speed. This is due to the flywheel acceleration andfriction torque which is along the axis of the flywheel and lines upwith the transducer measurement axis twice in one revolution of thegimbal. The fourth peak occurs at about 10 Hz which is the mechanicalresonance of the measurement system.

Embodiments of the present invention may provide several advantages. Forexample, the systems and methods may provide more effective techniquesfor assessing the performance of an actuator of an ACS, for both smalland large satellites. The systems and methods may provide suchassessment in a simplified, inexpensive, and easy to use manner.Moreover, the disclosed systems and methods enable assessment of theactuator without requiring motion of the support bracket assembly,thereby overcoming many of the shortcomings of conventional test beds.The actuator is also capable of operating about its full range ofmotion. In addition, the systems and methods may be adaptable for usewith different actuators (e.g., a CMG) and for one or multi-axis torquemeasurements. The systems and methods may also be employed in a varietyof environments.

System Design: Laser Sensor Embodiment

As noted herein, embodiments of the present invention are directed to asystem and method for assessing the performance of an ACS actuator suchas a CMG for small satellites (e.g., pico and nano-satellites). Theperformance of the actuator is sensed, such as through the output torqueusing a testing system, and then used in simulation of the spacecraftdynamic motion.

In another embodiment, a testing system is configured to use one or morelaser sensors to measure displacement of the gimbal(s) surroundingand/or supporting the CMG to thereby determine output torque of therelative axes. The system uses one or more high precision laserdisplacement sensors. One benefit of such an embodiment is that thelaser sensors have a larger effective dynamic range compared to thestrain gauge based sensors or transducers described in other embodimentsherein.

Similar to systems described above, torque transducer shafts may beattached to gimbals and/or a support bracket assembly surrounding theCMG (e.g., transducer shaft 80 shown in FIG. 6). In comparison toembodiments described above (e.g., FIGS. 6-7), the torque transducershaft coupled to a gimbal (e.g., the pitch axis gimbal 74 shown in FIG.6) may be replaced with a stiffer shaft and calibrated. When the CMGoutputs torque, the gimbal undergoes small angular deflection dependingon the stiffness of the calibrated shaft. The laser displacement sensormeasures this deflection, and since the stiffness of the shaft is known,the output torque can be correlated with the displacement of the gimbal.For example, the following set of equations illustrates the relationshipbetween the torque and the displacement of the gimbal.

Nomenclature:

δ Displacement of the gimbal

g Voltage to displacement gain

r Length of the gimbal arm

k _(t) Stiffness of the transducer shaft

θ Angular displacement of the gimbal

τ Torque on the gimbal

Equations:

τ−k_(t)θ  (6)

δ−r sin θ≈rθ  (7)

δ−gV   (8)

$\begin{matrix}{\tau = \frac{k_{t}{gV}}{r}} & (9)\end{matrix}$

The system design discussed below is for a single axis version with abuilt in capacity to be extended to a two axis version. The same conceptcan be extended to design two or more axis versions. Thus, although thediscussion below relates to a single axis system, the system may bemodified for use with a plurality of axes in alternative embodiments.

FIG. 22 shows a system 300 with a CMG 372 mounted thereon according toone embodiment of the present invention. The system 300 generallyincludes a support bracket assembly 371 and at least one sensor assembly373. The support bracket assembly 371 includes a pitch axis gimbal 374pivotally coupled to a roll axis gimbal 376. The pitch axis gimbal 374is configured to pivot with respect to the roll axis gimbal 376. Thepitch axis gimbal 374 is aligned in a generally vertical plane, whilethe roll axis gimbal 376 is aligned in a generally horizontal plane. Thegimbals 374, 376 may be made of various materials, such as aluminum, andare designed to have very low inertia. The pitch axis gimbal 374 ismounted inside the roll axis gimbal 376, wherein the gimbals may berectangular or other shapes with respective openings for accommodatingand supporting the CMG 372 therein. The pitch axis gimbal 374 comprisesan actuator mount bracket 388 to which the CMG 372 can be attached,thereby facilitating transfer of the output torque of the CMG 372 to thesupport bracket assembly 371. It is of note that the CMG 372 is capableof its full range of motion due to its positioning within the supportbracket assembly. Thus, the system 300 is configured for testing the CMG372 over its entire range of motion.

The pitch axis gimbal 374 and roll axis gimbal 376 may be coupled via apair of inner gimbal pivots 377 extending along a pitch axis of thesupport bracket assembly 371. In the illustrated embodiment, the innergimbal pivots 377 may be small stainless steel shafts coupled to thepitch axis gimbal 374. The shafts may be located on small low frictionbearings (e.g., a friction coefficient<0.01) mounted on the roll axisgimbal 376. One of the shafts, or transducer coupler shaft 380, may belonger than the other and projects through the roll axis gimbal 376.

The roll axis gimbal 376 is mounted on a pair of outer gimbal pivots 378along a roll axis of the support bracket assembly 371 in a similarmanner as the inner gimbal pivots 377. In this regard, the roll axisgimbal 376 is coupled to a support or U-shaped bracket 382 via the innergimbal pivots 378. However, the support bracket 382 is stationary and isfixed to a rigid isolated platform 384. The rotation of the roll axisgimbal 376 about pivots 378 may be locked using fasteners for a singleaxis measurement about the pitch axis. This locking can be removed toextend the testing to two-axis as explained in further detail below.

The sensor assembly 373 includes a laser sensor 390. The laser sensor390 may be positioned so as to point directly (e.g., along line 392) ata spot 391 on the pitch axis gimbal 374. In such a manner, the lasersensor 390 may measure displacement of the pitch axis gimbal 374 as thepitch axis gimbal 374 pivots about the pitch axis. Then, as noted above,the displacement measured can be used to determine the torque generatedabout the pitch axis. Thus, any torque generated about the pitch axis ismeasured by the laser sensor 390 while the support bracket assembly 371remains substantially motionless.

In some embodiments, a second laser sensor may be positioned so as tomeasure torque for of one or more other axes, such as the roll axis. Insuch an embodiment, the second laser sensor may be positioned to measuredisplacement of another gimbal, such as the roll axis gimbal 376.Furthermore, in embodiments of a three axis system, a third sensor canbe used to measure displacement of a yaw axis gimbal (e.g., yaw axisgimbal 288 shown in FIG. 21) and, thus, measure torque about the yawaxis.

A plot comparing the output torque of the strain gauge based torquetransducer (shown in FIG. 6) and the laser sensor (shown in FIG. 22)when the CMG is turned on is shown in FIG. 23. As can be seen in FIG.23, the strain gauge based torque transducer and the laser sensorgenerate similar results for measuring output torque. The laser sensorhas a very high dynamic range of 1.5×10⁶, which is defined as the ratiobetween the largest measurement and smallest measurement the sensor iscapable of reading. As such, the laser sensor has the ability to captureboth small and large changes in the displacement of the target gimbal(e.g., the pitch axis gimbal 374). Initial results have also shown thelaser sensor to be less prone to noise than the transducer-based testingsystem. Another benefit of use of the laser sensor is that a single setof laser sensors can be used for different classes of torque measurementby simply changing the calibrated transducer shaft. Further, the lasersensor permits un-attenuated measurements in the required bandwidth. Thehigh frequency dynamics can now be filtered out before it is used by aspacecraft dynamic model. As such, the development of a test bed may bebased on the use of these high performance sensors.

Attitude Determination Test Bed

In some embodiments, the testing system may comprise an attitudedetermination test bed (see e.g., the test bed shown in FIG. 1( b)).Indeed, in some embodiments, the sensors of the testing system may beused to measure precise output of the CMG (e.g., torque). This outputcan be inputted into a dynamic model of a spacecraft to propagate itsstates (e.g., attitude, position, velocity, and angular velocity).Further, the orbital disturbances based on the states of the spacecraftmay also be computed and input into the dynamic model. Indeed, in someembodiments, the attitude sensors (e.g., the torque sensor(s) and/orlaser sensor(s) described above) of the testing system may be used toprovide measured attitude information for the dynamic model.Additionally, in some embodiments, the testing system may be placedinside a thermal vacuum chamber to simulate a space-like environmentthat is controlled by a thermal model using the spacecraft orbitalposition and attitude. Moreover, since in some embodiments there is nolimitation of physical motion of the testing system, entire missionoperation models may be performed continuously, and realistic simulationcan be achieved.

In such a manner, the attitude determination test bed may be configuredto update a controlled dynamic environment being observed. The updatesmay be based on the orbital position and the attitude of the spacecraft,which are derived from the orbital model and attitude model (e.g.,example testing systems described herein) respectively. Examples includestar field simulators and magnetic field simulators.

With respect to a star field simulator illustrated in FIG. 24, oneapproach is to project a star map on a screen 410 within a shroudedenclosure 415, which the star tracker 425 will observe. The star map isdynamically updated based on the attitude of the satellite in thesimulation, as shown in FIG. 25. Multiple commercial products, such asmay be provided by Presagis and Mechdyne, are available for renderingthe star maps. Multiple star trackers based on the geometry of thespacecraft and the relative orientation of the star sensors can beincluded in the simulator. The output of the star Sensor, which is theestimated attitude quaternion, is used as the feedback for the attitudecontrol algorithms.

With respect to one embodiment of a magnetic field simulator shown inFIG. 26, the magnetic field simulator includes three sets of Helmholtzcoils 510, 511, 512 in a chamber, providing three-axis control. Thechamber size may be only large enough to accommodate flight magnetometerhardware 520 for the simulation. The Helmholtz coils 510, 511, 512 mayprovide a near uniform magnetic field in the center of the chamber,where the flight hardware is located. The magnetic field is measuredwith a lab magnetometer 530 for feedback, and controlled with acontroller (e.g., a LabView based controller), such as shown in FIG. 27.As the simulated attitude state of the satellite evolves in thesimulation, the Helmholtz coils 510, 511, 512 are driven to produce amagnetic field in the body frame of the flight magnetometer, based onthe World Magnetic Model (WMM). This arrangement of Helmholtz coils 510,511, 512 may also permit the cancellation of constant or slowly varyingspurious fields in the laboratory. Similarly, other simulators forvarious sensors can be built and their output used in a data fusionalgorithm to estimate the attitude of the spacecraft used for attitudecontrol.

As discussed above, some embodiments of the present invention includetesting systems for assessing the performance of an attitude controlsystem for small satellites. Such testing systems may provide advantagesover other testing systems (e.g., air bearing simulators). One advantageof example testing systems described herein is that many disturbancetorques are irrelevant. For example, bias torques and gravity gradienttorques can be compensated and a mass balancing system can be avoided.Further, aerodynamic torques are eliminated, as some example testingsystems can be placed in a thermal-vacuum chamber.

Another advantage to example testing systems described herein includesunlimited motion capability within the dynamic model since the testingsystem remains substantially motionless. Along these lines, exampletesting systems enable more realistic simulations that can account foradditional key elements, such as solar drag, atmospheric drag,third-body effect, gravity gradients, etc.

An additional advantage is that there is no need for an on-boardattitude feedback device with the testing system, according toembodiments of the present invention. Moreover, the testing system hasthe capability to test flight attitude determination hardware inconjunction with the attitude control test facility, thereby enabling anintegrated attitude determination and control test, which is notpossible on air bearing simulators.

Further advantages of example testing systems described herein includeincreased scalability and customization for a particular model. Alongthese lines, setup time for testing is decreased, as the testing systemis easier to adapt to different models. For example, using the setup fora spacecraft with different mass properties but the same actuatorsinvolves simply changing the parameters in the dynamic model.

Finally, as noted herein, a distinct benefit of embodiments describedherein includes the ability to more accurately test performance of smallsatellites. Indeed, small satellites are prone to minute disturbances,and the example testing systems described herein are designed to measurethese minute disturbances. Moreover, issues associated with miniaturemass balancing systems and attitude feedback devices are irrelevant.

Many modifications and other embodiments of the inventions set forthherein will come to mind to one skilled in the art to which theseinventions pertain having the benefit of the teachings presented in theforegoing descriptions and the associated drawings. Therefore, it is tobe understood that the inventions are not to be limited to the specificembodiments disclosed and that modifications and other embodiments areintended to be included within the scope of the appended inventiveconcepts. Although specific terms are employed herein, they are used ina generic and descriptive sense only and not for purposes of limitation.

REFERENCES

-   -   1. J. L. Schwartz, M. A. Peck, and C. D. Hall, “Historical        Review of Air-Bearing Spacecraft Simulators,” Journal of        Guidance, Control and Dynamics, Vol. 26, No. 4, 2003, pp.        513-522    -   2. Jung, D. and Tsiotras, P., “A 3-DoF Experimental Test-Bed for        Integrated Attitude Dynamics and Control Research,” AIAA        Guidance, Navigation, and Control Conference, Austin, Tex.,        2003, AIAA 2003-5331.    -   3. Kim, J. and Agrawal, B “Automatic mass Balancing of        Air-Bearing based Three-Axis Rotational Spacecraft Simulator,”        AIAA Journal of Guidance, Control, and Dynamics, Vol. 32, No. 3,        May-June 2009, pp. 1005-1017    -   4. Nagabhushan, V., “Development Of Control Moment Gyroscopes        For Attitude Control of Small Satellites”, Master's Thesis,        University of Florida, 2009    -   5. Kurukowa, H., “A Geometric Study of Control Moment        Gyroscopes”, PhD Thesis, University of Tokyo, 1998

That which is claimed:
 1. A system for assessing the performance of anactuator of an attitude control system (“ACS”) comprising: a supportbracket assembly coupled to an actuator of an ACS, the actuatorconfigured to generate an output torque; and at least one sensorassembly comprising a sensor configured to measure the output torqueabout at least one axis of the support bracket assembly while thesupport bracket assembly remains substantially motionless.
 2. The systemof claim 1, further comprising a data acquisition system incommunication with the at least one sensor assembly and configured toreceive the measured output torque.
 3. The system of claim 1, whereinthe support bracket assembly comprises a pitch axis gimbal coupled tothe actuator.
 4. The system of claim 3, wherein the support bracketassembly comprises a roll axis gimbal pivotably coupled to the pitchaxis gimbal.
 5. The system of claim 4, wherein the pitch axis gimbal andthe roll axis gimbal extend in perpendicular planes with respect to oneanother.
 6. The system of claim 4, wherein the at least one sensorcomprises a pitch axis sensor coupled to the pitch axis gimbal andconfigured to measure torque on the pitch axis gimbal.
 7. The system ofclaim 6, wherein the sensor assembly further comprises a shaft extendingthrough the roll axis gimbal and coupling the pitch axis gimbal and thepitch axis sensor.
 8. The system of claim 6, wherein the sensor assemblyfurther comprises a pitch axis sensor bracket coupled to the roll axisgimbal and configured to support the pitch axis sensor.
 9. The system ofclaim 6, wherein the at least one sensor assembly comprises a roll axissensor coupled to the roll axis gimbal and configured to measure torqueon the roll axis gimbal.
 10. The system of claim 9, wherein the supportbracket assembly further comprises a support bracket, and wherein theroll axis gimbal is pivotably coupled to the support bracket.
 11. Thesystem of claim 10, wherein the at least one sensor assembly furthercomprises a shaft extending through the support bracket and coupling theroll axis gimbal and the roll axis sensor.
 12. The system of claim 10,wherein the at least one sensor assembly further comprises a roll axissensor bracket coupled to the support bracket and configured to supportthe roll axis sensor.
 13. The system of claim 4, wherein the pitch axisgimbal is mounted internally with respect to the roll axis gimbal. 14.The system of claim 4, wherein the at least one sensor comprises a lasersensor configured to measure displacement of the pitch axis gimbal,wherein the displacement of the pitch axis gimbal is representative ofthe output torque on the pitch axis gimbal.
 15. The system of claim 14,wherein the at least one sensor assembly further comprises a secondlaser sensor configured to measure displacement of the roll axis gimbal,wherein the displacement of the roll axis gimbal is representative ofthe output torque on the roll axis gimbal.
 16. The system of claim 1,wherein the at least one sensor assembly is configured to measure theoutput torque about a plurality of axes of the support bracket assemblywhile the support bracket assembly remains substantially motionless. 17.The system of claim 1, wherein the actuator comprises a control momentgyroscope (CMG).
 18. The system of claim 1, wherein the support bracketassembly is configured to deflect less than about 30 arc minutes whilethe sensor measures the output torque about the at least one axis. 19.The system of claim 1, wherein the at least one sensor assemblycomprises a laser sensor configured to measure displacement of at leasta portion of the support bracket assembly, wherein the displacement ofthe portion of the support bracket assembly is representative of theoutput torque about at least one axis of the support bracket assembly.20. The system of claims 1, wherein the at least one sensor assemblycomprises a torque sensor coupled to at least a portion of the supportbracket assembly and configured to measure the output torque.
 21. Amethod for assessing the performance of an actuator of an attitudecontrol system (“AC S”) comprising: coupling an actuator of an ACS to asupport bracket assembly; generating an output torque with the actuator;and measuring the output torque about at least one axis of the supportbracket assembly with at least one sensor while the support bracketassembly remains substantially motionless.
 22. The method of claim 21,wherein measuring comprises measuring the output torque about aplurality of axes of the support bracket assembly.
 23. The method ofclaim 21, wherein the actuator comprises a control moment gyroscope(CMG).
 24. The method of claim 21, wherein measuring comprises measuringthe output torque about the at least one axis while the support bracketassembly deflects less than about 30 arc minutes.
 25. The method ofclaim 21 further comprising coupling the at least one sensor to at leasta portion of the support bracket assembly, wherein measuring comprisesmeasuring the output torque.
 26. The method of claim 21, whereinmeasuring comprises measuring the displacement of a portion of thesupport bracket assembly with a laser sensor, wherein the displacementof the portion of the support bracket assembly is representative of theoutput torque about at least one axis of the support bracket assembly.